Trajectories

Questionnaires

Items

Lexical frequency

Cognateness

Participants

Age

Language profile

Data analysis

We initially fitted a null model (fit_0) than only included the predictors age and frequency as nuisance parameters, along with random intercepts by id and item, and random slopes of frequency by id, and age by item, and their correlation parameter. We then extended this model (fit_1) to include the main effect of doe, and the doe by item random slope. Finally, we added the main effect cognate (fit_2), its interaction with doe (doe:cognate), and random slopes for cognate by id. The models were implemented in brms as:

• understands/produces ~ 1 + age + frequency + (1 + age | item) + (1 + frequency | id)
• understands/produces ~ 1 + age + frequency + doe + (1 + age + doe | item) + (1 + frequency | id)
• understands/produces ~ 1 + age + frequency + doe*cognate + (1 + age + doe | item) + (1 + frequency + cognate| id)

Model equation

R code (brms)

understands ~
1 + age + frequency + lp*cognate +
(1 + age + lp | te) +
(1 + frequency + cognate | id),
family =  bernoulli("logit")

Stan code

Stan code generated by brms::stancode:

Results

Vocabulary

Vocabulary size

Comprehension

Production

Short vs. Long

Comprehension

Production

Raw data

Prior-predictive checks

Model selection

We compared the performance of these models using Bayesian leave-one-out cross-validation (LOO) using the loo and loo_compare functions of the brms R package (dependent of the LOO R package). LOO consists in computing the average likelihood of each observation after estimating the model’s parameters leave that same observation out of the data set. Although the loo function uses a particular algorithm that speeds up the computation of this criterion (pareto-smooth importance sampling, PSIS), the size of our data set lead us to rely on the computation of the same criterion using a sampling approach via de loo_subsample function.

Fixed effects

      ESS: Effective sample size
      <br />
    </p>
    <p style="margin: 0px; font-size: 90%; padding: 4px;">
      <sup style="font-style: italic; font-size: 65%;">
        <em>2</em>
      </sup>
       
      Transformed using the inverse logit to get the average probability of correct response
      <br />
    </p>
    <p style="margin: 0px; font-size: 90%; padding: 4px;">
      <sup style="font-style: italic; font-size: 65%;">
        <em>3</em>
      </sup>
       
      Transformed using the divide-by-four- rule to get the maximum change in probability of correct response, associated with a unit increase in this variable.
      <br />
    </p>
  </td>
</tr>

Random effects

Participant

Item

Marginal means

Area under the curve (AUC)

Traceplots